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Optimal lower bounds for cubature error on the sphere S2 by Kerstin Hesse; Ian H. Sloan is a Mathematics article available to read on EtoBox.
What is Optimal lower bounds for cubature error on the sphere S2 about?
We show that the worst-case cubature error E(Q m ; H s ) of an m-point cubature rule Q m for functions in the unit ball of the Sobolev space H s =H s (S 2 ), s > 1, has the lower bound E(Q m ; H s ) c s m -s 2 , where the constant c s is independent of Q m and m. This lower bound result is optimal, since we have established in previous work that there exist sequences 2 with a constant cs independent of n. The method of proof is constructive: given the cubature rule Q m , we construct explicitly a 'bad'function f m ∈ H s , which is a function for which Q m f m =0 and f m -1 The construction uses results about packings of spherical caps on the sphere.
Who reads Optimal lower bounds for cubature error on the sphere S2?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- Kerstin Hesse; Ian H. Sloan
- Publisher
- Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0885-064X)
- Published
- 2005
- Language
- EN
- Field
- Mathematics (Physical Sciences)